The National Highway Traffic Safety Administration estimates that 6,764,000 police-reported motor vehicle traffic accidents occurred in the United States in 1997 alone, killing 41,967 and injuring 3,399,000 persons. Unfortunately, each of these traffic accidents often is the beginning in a chain of medical and legal wrangles, which exact a great economic and emotional toll on the accident victims, their families, and society as a whole. As a result, highway safety has become a top priority for the nation.
In an effort to improve our understanding of these accidents, vehicle collisions often are reconstructed using one of several known methods. As a result of these analyses, scientists and engineers are able to make appropriate improvements to highway infrastructure and vehicle design, insurance companies are able to settle claims and manage risk, and courts of law are able to adjudge liability in grievances brought by accident victims.
Before the advent of computing technologies, collisions typically were modeled using known exit or entry conditions, and applying either conservation of momentum or energy principles to solve for unknown parameters. The advent of computing technologies has engendered a new breed of collision analysis, referred to as collision simulation, by which scientists and engineers may look inside a collision and simulate the mechanics of the collision over a large number of discrete time steps. After initial parameters, such as size, mass, position, and velocity of the colliding objects, are input into a collision simulation program for each body, the collision simulation program typically positions each of the bodies, and calculates the collision and external forces acting on each body at each time step.
Collision simulation commonly is practiced using finite element methods, which divide up each of the bodies into a large number of discrete subregions, or finite elements, and calculate the forces acting on each of the finite elements due to transfer of momentum, heat energy, etc., occurring along boundaries with neighboring elements. By examining the collision at each of a large number of finite regions, the overall collision can be simulated for objects having truly arbitrary geometries, thus making finite element analysis extremely powerful as compared to prior solution techniques. In addition, finite element methods typically also include algorithms to model certain phenomena, such as buckling, that depend on non-local geometric properties of the colliding objects.
Finite element collision methods utilize contact algorithms to manage behavior of the elements as they collide. Following movement of the meshes, the contact algorithms perform two essential functions for each element: location and restoration. During location, the position of the element relative to other surface elements is ascertained. During restoration, position and/or topology of the element within the mesh is altered, due to contact with other elements, and forces associated with the alteration of the mesh are calculated based on the mass of each element, according to conservation of momentum principles.
Current finite element contact algorithms typically alternate treating one of the meshes as a master mesh and the other of the meshes as a slave mesh. During a collision, nodes of the slave mesh that penetrate the master mesh are repositioned to conform to the surface of the master mesh. As the slave mesh and master mesh alternate, each mesh conforms to the other, and realistic collision behavior may be simulated.
For example, in A New Interaction Algorithm with Erosion for Epic-3, published in U.S. Army Ballistic Research Laboratory Report BRL-CR-540 (February 1985), Ted Belytshchko discloses a method of modeling collisions that searches for penetration of a master surface by a slave node and restores the position of the slave node onto the master surface. The velocity of the restored slave node has been modified according to its new position. The change in momentum experienced by the slave node due to the restoration of its position onto the master surface is apportioned to the master nodes defining the master surface element.
In A General-Purpose Contact Detection Algorithm for Non-Linear Structural Analysis Codes, published as Sandia Report 92-2141 (May 1993) available from the National Technical Information Service of Springfield, Va., Heinstein et al. disclose a method of collision simulation that uses a global contact search and a detailed contact search involving the projected motion of both the master and slave surfaces. Penetrating slave nodes then are accelerated out of the master surface with a force proportional to the penetration distance.
Several problems exist with using these contact algorithms to conduct a finite element simulation of a collision. First, each method requires development of a complex three-dimensional structural mesh, which may require weeks of engineering time. The mesh must not only accurately reflect the outer geometry of the object, but also must reflect internal geometry of the object. In addition, the mesh must be constructed to represent material properties of the object at each element, such that the finite element method may calculate various physical quantities based on functional interdependencies between the elements. In particular, each element of the mesh must have an associated mass, such that the method may solve a conservation of momentum equation for each collision between elements, from which solution other physical quantities, such as acceleration, shear, etc., may be derived. Development of such a complicated mesh is both time consuming and expensive.
Second, finite element methods often require significant amounts of computer processing time. A finite element model must conduct calculations to solve for unknown parameters for each element, resulting in a complex system of equations with a large number of unknowns. A small finite element model constructed to simulate static behavior of objects typically may generate a set of ten thousand equations, which are solvable in a reasonable amount of time by a personal computer. To simulate a dynamic collision, such as a vehicle collision, this set of equations must be solved for each of a large number of time steps, typically generating several hundred thousand or millions of equations and requiring a mainframe and/or supercomputer to run.
Because of the time and effort involved in building a mesh, and the cost of processing time on a mainframe or supercomputer, finite element methods typically only are practical for projects with large budgetary resources, such as vehicle design and manufacture. Finite element methods remain impractical for smaller budget projects, such as reconstruction of everyday vehicular accidents, marine accidents, landslides, demolition and ballistic tests, manufacturing processes, etc. Currently, only a very small number of these collisions are reconstructed using traditional finite element methods. It would be desirable to provide a collision simulation method capable of handling arbitrary geometries, yet which does not require a great amount of preparation time, and which may be executed in a few minutes on a personal computer, such that a greater number of these collisions may be reconstructed at a lower cost, in less time.